Download Defining Genetic Diversity (within a population)

Primer in Population Genetics
Hierarchical Organization
of Genetics Diversity
Primer in Population Genetics
Defining Genetic Diversity
within Populations
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•
•
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Polymorphism – number of loci with > 1 allele
Number of alleles at a given locus
Heterozygosity at a given locus
Theta or θ = 4Neμ (for diploid genes)
where
Ne = effective population size
μ = per generation mutation rate
Defining Genetic Diversity
Among Populations
• Genetic diversity among populations occurs if
there are differences in allele and genotype
frequencies between those populations.
• Can be measured using several different metrics,
that are all based on allele frequencies in
populations.
– Fst and analogues
– Genetic distance, e.g., Nei’s D
– Sequence divergence
Estimating Observed Genotype and
Allele Frequencies
•Suppose we genotyped 100 diploid individuals (n = 200 gene
copies)….
Number
Genotype Frequency
Genotypes
AA
Aa
aa
58
40
2
0.58 0.40 0.02
# obs. for genotype
Allele
AA Aa aa
Observed Allele Frequencies
A
116 40 0
156/200 = 0.78 (p)
a
0 40 4
44/200 = 0.22 (q)
Estimating Expected Genotype Frequencies
Mendelian Inheritance
Mom
Aa
•Offspring inherit one
chromosome and thus
one allele independently
and randomly from each
parent
•Mom and dad both
have genotype Aa,
their offspring have
three possible
genotypes:
AA
Aa
Dad
Aa
A
Mom
Aa
A
A
AA
Mom
Aa
a
Aa
Dad
Aa
a
Dad
Aa
A
Mom
Aa
Dad
Aa
a
a
aa
Aa
aa
Estimating Expected Genotype Frequencies
•Much of population genetics involves manipulations of equations that have a
base in either probability theory or combination theory.
-Rule 1: If you account for all possible events, the probabilities sum to 1. [e.g.,
p + q = 1 for a two-allele system].
-Rule 2: The probability that two independent events occur is the product of
their individual probabilities.
[e.g., probability of a homozygote with aa genotype is q*q = q2].
•Thus, under “ideal” conditions, expected genotype frequencies are p 2 for AA,
2pq for Aa, and q2 for aa; and the genotype frequencies sum to 1 such that:
p2 + 2pq +and q2 = 1 (Hardy Weinberg Equilibrium)
Expected Genotype Frequencies
under HWE
Testing for Deviations from HWE
Genotypes
AA
Aa
aa
Total
Observed numbers (O)
16
20
4
40
s
Expected frequencies
p2
0.652
0.42
2pq
2*0.65*0.35
0.46
p2
0.352
0.12
1.0
1.0
1.0
Expected numbers (E)
17
18
5
40
(expected frequency * 40)
p = 52/80 = 0.65
q = 28/80 = 0.35
Testing for Deviation from HWE
with a Chi-square test
χ2 = Σ (O – E)2/E
χ2 = (16–17)2/17 + (20–18)2/18 + (4–5)2/5
χ2 = 0.4
• Probability of obtaining a χ2 of 7.2 or greater (1
df) = 0.53
• Thus, observed genotypes do not deviate from
HWE
Estimating Expected Heterozygosity
when >2 Alleles
• When there are more than 2 alleles, a simple way to
calculate HW expected heterozygosity is:
He = 1 – Σ pi2
• For example, if allele frequencies for 3 alleles are 0.5,
0.3, and 0.2, HW expected heterozygosity is:
He = 1 – (0.52 + 0.32 + 0.22) = 1 – (0.25 + 0.09 + 0.04)
= 0.62
Estimating Genomic Diversity
• To fully assess the demographic history and
evolutionary potential of species, genome-wide
assessment of genetic diversity is needed
(mammals have ~35,000 loci).
• Genetic diversity measures are estimated over
several loci that are presumed to be a random
sample of the genome
• Heterozygosity is often averaged over multiple
loci to obtain an estimate of genome-wide
genetic diversity
Evolutionary Processes that Influence
Genetic Diversity
•Genetic Drift – random change in allele frequencies in a population from
generation to generation due to finite population size.
•Mutation – an error in the replication of DNA that causes a structural
change in a gene. Only source of new genetic variation in populations (sex
cells only).
•Gene Flow – exchange of genetic information among population via
migration of individuals.
•Natural Selection – differential contribution of genotypes to the next
generation due to differences in survival and reproduction.
Genetic Drift
Random changes in allele frequencies across generations due to
finite population size
Gametes
(many)
Breeding
Individuals (2)
a
A
Aa
a
A
a
a
a
AA
a
A
A
Gen 1
A
Gen 2
a
Aa
Aa
Breeding
Individuals (2)
a
A
A
A
a
Gametes
(many)
Breeding
Individuals (2)
A
A
a
A
A
a
Gen 3
A
AA
A
A
A
A
a
AA
A
A
A
PA = 0.5
PA = 0.75
PA = 1.0
Pa = 0.5
Pa = 0.25
Pa = 0
Genetic Drift
•Allele frequencies change over time randomly and some alleles can go
extinct or become “fixed”.
•Which alleles frequencies can “drift” in different directions for different
populations, resulting in greater differences among populations
1
p (frequency of allele a)
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
5
10
Time (generations)
15
20
Loss of Allelic Diversity
Probability of Losing Allele
•The probability of an allele being lost during a bottleneck
of size Ne: (1 – p)2Ne, where p is the frequency of the allele,
in the generation following the bottleneck
1
p
0.8
Rare alleles are
lost first during
bottlenecks
0.01
0.1
0.5
0.6
0.4
0.2
0
0
100
200
Effective Population Size
300
Loss of Heterozygosity
•Loss of heterozygosity occurs due to the loss of
alleles, but occurs more slowly, particularly
compared to rare alleles.
•Per generation loss of heterozygosity (increase in
homozygosity) = 1/2Ne
•Over t generations, the loss of heterozygosity =
1 – (1 – 1/2Ne)t
Loss of Genetic Diversity in Small Populations
Theoretical Expectations
Mutations
• Mutation – an error in the replication of DNA that
causes a structural change in a gene.
– Entire chromosomal complements
– Translocations: the movement of nucleotides from one
part of the genome to another.
– Duplication: small number of nucleotides or large pieces
of chromosomes
– Single nucleotides: removals, substitutions, or insertions
• E.g., a substitution…
Mutations
•Mutations can offset loss of genetic diversity due to genetic drift,
but mutation rates in nature are low, ~10-9 mutations per locus per
generation in protein coding nuclear genes.
Frequency of Allele A
•Also, most mutations are harmful and get weeded out of the
population, relatively few mutations are beneficial
Mutation occurs, generating
allele A
---- Beneficial mutation
---- Harmful mutation
0
Time (generations)
Selection
•Whether selection increases within-population diversity
depends on if selection is stabilizing, disruptive, or directional
AA
•Whether selection
increases withinpopulation diversity
also depends on if
selection is stabilizing,
disruptive, or
directional
AA
Aa
Aa
aa
aa
Frequency of Phenotype
AA
Aa
aa
Selection
•In populations of finite size, selection is not the only factor
responsible for changes in allele and genotype frequencies.
•For example, stochastic fluctuations occur in the frequency of
allele A due to genetic drift, despite a general increase due to
directional selection.
1
0.9
p
p (frequency of allele a)
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
5
10
Time (generations)
Generations
15
20
Gene Flow
•Increases genetic variation within populations because it brings
in new alleles.
•Reduces genetic differences among populations, because alleles
are being exchanged
•E.g., Five populations with different initial frequencies (p) of
allele a connected by a migration rate (m) of 0.05.
1
subpop1 (p0 = 1)
p (frequency of allele a)
0.9
subpop2 (p0 = 0.75)
0.8
subpop3 (p0 = 0.5)
0.7
subpop4 (p0 = 0.25)
0.6
subpop5 (p0 = 0)
0.5
0.4
0.3
0.2
0.1
0
0
20
40
60
Time (number of generations)
80
100
Evolutionary Processes that Influence
Genetic Diversity
Level of Genetic Variation
Within Pops
Among Pops
Genetic Drift
↓
↑
Mutation
↑
↑
Gene Flow
↑
↑
Selection
↑↓
↑↓
Potential Effects of Habitat Fragmentation on
Genetic Diversity
•Disrupting gene flow
between population A
and B and fragmenting
habitat between A and
C reduces genetic
variation in A and C.
•Ultimately allele t or T
and allele s or S gets
“fixed” in populations B
and C.
Increase in Genetic Variation
among Populations